Two equations are given below: m + 5n = 20 m = n − 4 What is the solution to the set of equations in the form (m, n)? (3, 7) (0, 4) (5, 1) (2, 6)

x+2/x+9 is the simplified form of x squared minus 10 x minus 24 all over x squared minus 3 x minus 108 and x≠-2 and x≠-9 are the restrictions of the variable.

Two or more expressions with an Equal sign is called as Equation.

The given sentence is x squared minus 10 x minus 24 all over x squared minus 3 x minus 108

(x²-10x-24)/(x²-3x-108)

We will simplify  the given expression by factorisation we will get

(x²-12x+2x-24)/x²-12x+9x-108

Taking x as common from first two terms in numerator and 2 from last two terms in numerator

Similarly, take x common from first two terms and 9 from last two terms in denominator we will get

x(x-12)+2(x-12)/x(x-12)+9(x-12)

(x+2)(x-12)/(x+9)(x-12)

After simplifying we are left with x+2/x+9

the restrictions on the variable is x should not be equal to -9 and it should not be -2

Hence, x+2/x+9 is the simplified form of x squared minus 10 x minus 24 all over x squared minus 3 x minus 108 and x≠-2 and x≠-9 are the restrictions of the variable.

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We can solve for the value of x using the formula:

V = l w h

where,

h = x the size of the cut since it would form the walls of the rectangle

w = 8.5 – 2x        = it is subtracted by 2x since two sides will be cut

l = 11 – 2x

Substituting:

V = x (8.5 − 2x) (11 − 2x)

Expanding the expression:

V = 93.5 x – 39 x^2 + 4 x^3

To solve the maxima, we have to get the 1st derivative dV / dx then equate to 0. dV / dx = 0:

dV / dx = 93.5 – 78 x + 12 x^2

0 = 93.5 – 78 x + 12 x^2

We get:

x ≈ 1.585 in          and        x ≈ 4.915 in

Therefore Anya’s suggestion of 1.5 inches would create the larger volume since it is nearer to 1.585 inches.

There can be different volumes since volume refers to the amount of space inside the rectangle. They can only have similar perimeter and surface area, but not volume.

 It is restricted to 0 in. < x < 4.25 in. because our w is 8.5 – 2x. Going beyond that value will give negative dimensions.

250.

To determine the 4th term in a geometric sequence, start with the first term and use the common ratio. In this case, the first term is -2 and the common ratio is -5. The formula for finding the nth term of a geometric sequence is an = a1 * r(n-1).

Identify the values: a1 = -2, r = -5, n = 4.

Substitute into the formula: a4 = -2 * (-5)(4-1).

Calculate the 4th term: a4 = -2 * (-5)3 = -2 * (-125) = 250.

For the quarts to cups:

First, you need to figure out how many cups are in 1 quart. This is 4 cups = 1 quart.

If you have 4 cups in one quart then you need to multiply 4 cups by 5 quarts which equals 20 cups.

For the cups to gallons, you first need to find out how many cups are in 1 gallon. This is 16 cups = 1 gallon.

If you have 16 cups in 1 gallon then you will need to multiply 48 cups by 16 to find out how many gallons you will have which equals 3 gallons.

Hope this helps.

Final answer:

To determine the ways to receive change for a ten-dollar bill when you have spent $9.74, you need to consider the coin denominations that sum up to the remaining $0.26. This is a combinatorial problem known as the 'coin changing problem,' which involves calculating the combinations of coins that can be used to make up the remaining change.

Explanation:

To calculate how many ways you can receive change for a ten-dollar bill, you would need to consider the different denominations of U.S. currency and how they could combine to total the difference between your purchase amount of $9.74 and a $10 bill, which is $0.26.

The ways you can receive change can include a combination of quarters, dimes, nickels, and pennies.

To model this as a mathematical problem, let's calculate the different combinations: You could receive one quarter and one penny, or two dimes and six pennies, or one dime, one nickel, and eleven pennies, and so on.

Since the question asks for the number of ways to receive change and not the specific combinations, we can use combinatorics to determine the total number of combinations.

Note:

Since the actual calculations for combinatorics can be complex and the question does not provide all the necessary details to give a definitive number, we can consider this as an example of a combinatorial problem in mathematics.

The coin changing problem is a classic example that could be applied here, where algorithms can be used to find the number of ways to make change for a certain amount using given denominations.

The probability of flipping a coin and it showing heads and drawing a diamond from a standard deck of cards is 1/8.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability = (number of sides with a head / number of sides of a coin) x (number of diamonds / number of cards)

1/2 x 13/54 = 1/8

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Final answer:

The probability of flipping a coin and getting heads followed by drawing a diamond from a standard deck of cards is 1/8 or 0.125.

Explanation:

The probability question involves two independent events: flipping a coin and drawing a card from a standard deck. For the coin toss, the probability of getting heads is 0.5 since a coin has two sides and both are equally likely. Now, for drawing a diamond from a standard deck of cards, there are 13 diamonds out of 52 cards, so the probability is 13/52 or 1/4.

To find the probability of both events happening, we multiply the probabilities of each event, because they are independent events. So, the probability of flipping a coin and getting heads and then drawing a diamond is (1/2) * (1/4) = 1/8 or 0.125.

x+y = 4

x=4-y

52x+50y=204

52(4-y)+50y=204

208-52y+50y=204

208-2y=204

-2y=-4

y=2

x= 4-2=2

check 52*2=104

50*2 = 100

104+100=204

 so he traveled 2 hours at both 50 and 52 mph

To find the inverse of a function, replace f(x) with y, swap x and y, then solve for y. Thus, the inverse of f(x) = x + 5 is f^-1(x) = x - 5.

To find the inverse of a function like f(x) = x + 5, we use the following steps:

Replace the function notation f(x) with y. So, we get y = x + 5.

Swap the roles of x and y. This changes the equation to x = y + 5.

Solve for y to get the inverse function. By subtracting 5 from both sides, we acquire y = x - 5.

This implies that the inverse of the function f(x) = x + 5 is f-1(x) = x - 5.

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The greatest amount of money that rounds to $105.40 is $105.41, while the least amount that rounds to $105.40 is $105.39.

The greatest amount of money that rounds to $105.40 would be the amount slightly greater than $105.40. Since rounding to the nearest cent, we would look at the hundredths place. Any amount greater than $105.405 would round up to $105.41. So the greatest amount of money that rounds to $105.40 would be $105.41.

The least amount of money that rounds to $105.40 would be the amount slightly less than $105.40. Again, looking at the hundredths place, any amount less than $105.395 would round down to $105.39. So the least amount of money that rounds to $105.40 would be $105.39.

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-225 divided by -15 is equal to 15.

A division is a process of splitting a specific amount into equal parts.

We have to find the value of the expression -225 divided by -15

By means of division we can find this value.

-225/(-15) = 15

Two hundred twenty five is the numerator and fifteen is the denominator.

We get 15

When we divide a negative number by a negative number, the result is a positive number.

Therefore, -225 divided by -15 is equal to 15.

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Final answer:

The inequality that represents the speed of the car while cruise control is being used is 62 ≤ s ≤ 68, where s is the car's speed and it shows the car's speed will be at least 62 mph and at most 68 mph.

Explanation:

The cruise control feature on a car is designed to maintain a steady speed, in this case, 65 miles per hour. However, it is acknowledged that the car's actual speed can fluctuate slightly. The question asks for an inequality that represents the potential speed of the car while cruise control is in use.

Considering the car's speed can vary by up to 3 mph more or less than the cruise control setting, we can set up an inequality to describe this range of speeds. The car's speed (s) should be no more than 3 mph above 65 mph and no less than 3 mph below 65 mph. Therefore, the inequality that represents the speed s of the car would be:

62 ≤ s ≤ 68

This inequality shows that the car's speed will be at least 62 mph and at most 68 mph, encompassing the 3 mph range of variation allowed by the cruise control setting.

Answer:

Use the formula.

The circumference of a circle is found with the formula C= π*d = 2*π*r. Thus pi equals a circle's circumference divided by its diameter. Plug your numbers into a calculator: the result should be roughly 3.14

Step-by-step explanation:

Answer:

Answer is 5.

Step-by-step explanation:

The given expression is :

[tex]4x^{3}y+8x^{2} +6x+5[/tex]

We have to tell the constant term here.

A constant term is one that remains same and does not change with change in values of x and y.

Here, other terms contains either x or y or both, that will change with change in x and y. Only 5 is the single term that will remain constant.

So, the answer is 5.

So what we do to one side of the equal sign, we must do to the other side as well.

We want to solve for f, so we need to subtract 15 on both sides of the equal sign in order to get f alone by itself on the left side:

[tex] f=20 [/tex]

So now we know that f = 20.

f + 15 = 35

Isolate the variable (f). Note the equal sign. What you do to one side, you do to the other.

Subtract 15 from both sides

f + 15 (-15) = 35 (-15)

f = 35 - 15

Simplify

f = 20

f = 20 is your answer

hope this helps

Answer:

[tex](6x^\frac{13}{2})[/tex]

Step-by-step explanation:

[tex](2x^6)(3x^\frac{1}{2})[/tex]

Use property of exponents

a^m * a^n = a^mn

When the exponents with same base are in multiplication then we add the exponents

2 times 3= 6

now we multiply x^6 and x^1/2

[tex](x^6)(x^\frac{1}{2})=x^{6+\frac{1}{2}}[/tex]

Make the denominators same to add the fractions

[tex]\frac{12}{2} +\frac{1}{2} =\frac{13}{2}[/tex]

[tex](6x^\frac{13}{2})[/tex]

Answer:

1/2

Step-by-step explanation:

no guarantees but the guy before me said 10/20 and of course if you divide 10 and 20 you get 0.5, and 0.5 is equal to 1/2.

A. The point estimate of μ1 − μ2 is calculated using the value of x1 - x2, therefore:

μ1 − μ2 = x1 – x2 = 7.82 – 5.99

μ1 − μ2 = 1.83

B. The formula for confidence interval is given as:

Confidence interval = (x1 –x2) ± z σ

where z is a value taken from the standard distribution tables at 99% confidence interval, z = 2.58

and σ is calculated using the formula:

σ = sqrt [(σ1^2 / n1) + (σ2^2 / n2)]

σ = sqrt [(2.35^2 / 18) + (3.17^2 / 15)]

σ = 0.988297

Going back to the confidence interval:

Confidence interval = 1.83 ± (2.58) (0.988297)

Confidence interval = 1.83 ± 2.55

Confidence interval = -0.72, 4.38